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in excercises 9-12, write an equation of the line that passes through the given point and is parallel to the given line. #10 and #12

In Excercises 912 Write An Equation Of The Line That Passes Through The Given Point And Is Parallel To The Given Line 10 And 12 class=

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Heatheridn

#10 Answer:

     y = -5x + 7

Step-by-step explanation:

     A line that is parallel will have the same slope. Then, we can use the given coordinate point to write a point-slope form equation. After that, we will rewrite the equation in the same form as the given equations. This looks to be a slope-intercept form equation, but with a coefficient on y to avoid fractions.

Given:

  y = -5x + 4 at the point (1, 2)

Parallel lines, same slope:

  m = -5

Point-slope form equation:

  y - y1 = m(x - x1)

  y - 2 = -5(x - 1)

Distribute and add 2 to both sides:

  y = -5x + 5 + 2

Addition:

  y = -5x + 7

#12 Answer:

     2y = 3x - 16

Step-by-step explanation:

     We will follow the same steps as above to find the parallel line through the given point.

Given:

  2y = 3x + 10 at the point (2, -5)

Parallel lines, same slope:

  m = 3/2

Point-slope form equation:

  y - y1 = m(x - x1)

  y - - 5 = 3/2(x - 2)

Simplify and distribute:

  y + 5 = 3/2x - 3

Subtract 5 from both sides:

  y = 3/2x - 8

Multiply both sides by 2 to remove the fraction:

  2y = 3x - 16

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